One of the major measures of the quality of service provided byany organization is the speed with which it responds to customercomplaints. A large family-held department store selling furnitureand flooring, including carpet, had undergone a major expansion inthe past several years. In particular, the flooring department hadexpanded from 2 installation crews to an installation supervisor, ameasurer, and 15 installation crews. The store had the businessobjective of improving its response to complaints. The variable ofinterest was defined as the number of days between when thecomplaint was made and when it was resolved. Data were collectedfrom 40 complaints that were made in the past year(furniture2.xlsx). (a) The installation supervisor claims that themean number of days between the receipt of a complaint and theresolution of the complaint is 30 days. To test the claim, buildnull and alternative hypotheses (for a two-tail test). (b) Toconduct a two-tail t test based on the hypotheses in (a), identifythe rejection regions (two sides) given the 99% critical level. (c)Using the given data, compute the test statistic for the t test.(d) At the 0.01 level of significance, should the claim be rejected(i.e., the mean number of days is different from 30)? In thecritical-value approach, what is your conclusion based on (b) and(c)? Explain. (e) Using the test statistic in (c), determine thep-value for the t test. (f) In the p-value approach, what is yourconclusion based on (e)? Explain.

Days
65
43
35
137
31
27
152
22
123
81
74
27
11
19
126
110
110
29
61
35
94
31
26
5
12
4
165
32
29
28
29
26
25
1
14
13
13
10
5
27